Three-dimensional numerical simulations are successfully carried out on thermo-hydraulic characteristics of a new plain fin-and-elliptical tube (PFET) heat exchanger with innovative types of tube-banks, namely-a slotted elliptical tube-bank (SETB) (Case B and Case C) and a slotted annular elliptical tube-bank (SAETB) (Case D and Case E). The new PFET heat exchanger contains elliptical cross-sectioned tubes that create narrow slots oriented in the streamwise or/and spanwise direction. The investigation on the effects of different shape tube-banks on the air-side heat transfer and fluid flow characteristics in the new PFET heat exchanger was performed using the ANSYS CFX (R) package. The objectives of this investigation are to determine an optimal staggered tube-bank configuration for augmenting heat transfer rates with minimal pressure drop penalties, and compare the results against traditional non-slotted elliptical tube-bank heat exchangers. The averaged heat transfer rate of the SETB/SAETB heat exchanger is more than 15% greater than that of the traditional non-slotted elliptical tube heat exchanger. The overall performance evaluation criteria, estimated in terms of the area goodness factor and volume goodness factor for enhanced cases (SETBs/SAETBs), were higher than there found by a non-slotted elliptical tube-bank case. Overall, the computational results showed that the Case D causes an appreciable increase of the heat transfer rate without a pressure drop penalty.